Finite Group Databasebeta

← #1089589

Subgroups — #1089589

Order 512.

2744 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2427C211yesmaximal, characteristic
2C2×#2325C211yesmaximal, characteristic
3#16429C212yesmaximal, complemented
4#16365C211yesmaximal, characteristic, complemented
5#16066C212yesmaximal, complemented
6#15954C212yesmaximal, complemented
7#15541C212yesmaximal, complemented
8#15454C212yesmaximal, complemented
9#15383C212yesmaximal, complemented
10#15339C212yesmaximal, complemented
11#15063C211yesmaximal, characteristic, complemented
12#14934C211yesmaximal, characteristic, complemented
13#14860C212yesmaximal, complemented
14#14767C212yesmaximal, complemented
15#14473C212yesmaximal, complemented
16#14417C211yesmaximal, characteristic
17#14040C211yesmaximal, characteristic, complemented
18#14016C212yesmaximal, complemented
19#13975C212yesmaximal, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25#2427—28no—
26C2×#400C2212yes—
27C2×#398C2212yes—
28C2×#397C2212yes—
29C2×#394C2212yes—
30#2325—28no—
31C2×#391C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#388C2212yes—
34C2×#387C2212yes—
35C2×#387C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#385C2212yes—
42C2×#385C2211yescharacteristic
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#381C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2212yes—
52#1446C2212yes—
53#1446C2212yes—
54#1445C2212yes—
55#1445C2212yes—
56#1445C2211yescharacteristic
57#1445C2212yes—
58#1445C2212yes—
59#1445C2212yes—
60#1445C2211yescharacteristic
61#1444C2212yes—
62#1444C2211yescharacteristic
63#1443C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1442C2212yes—
74#1442C2211yescharacteristic
75#1441C2212yes—
76#1441C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1438C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1434C2212yes—
94#1434C2212yes—
95#1434C2212yes—
96C22⋊#95C2211yescharacteristic
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2212yes—
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2211yescharacteristic
109C23×Q8C2311yescharacteristic
110C23×D4C2312yes—
111C23×D4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C24×C4C2312yes—
117C24×C4C2311yescharacteristic
118C2×#124—24no—
119C2×#124—28no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—44no—
122C2×#121—28no—
123C2×#121D418yes—
124C2×C4×D4—28no—
125C2×C4×D4—24no—
126C2×C4×D4—44no—
127C2×C4×D4—44no—
128C2×C4×D4—44no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160#400—44no—
161#398—44no—
162#397—28no—
163#394—28no—
164#391—24no—
165#389—24no—
166#388—28no—
167#387—28no—
168#387—44no—
169#386—28no—
170#386—28no—
171#386—28no—
172#386—28no—
173#386—28no—
174#385—28no—
175#385—24no—
176#385—44no—
177#385—44no—
178#381—44no—
179#380—24no—
180#380—28no—
181#380—44no—
182C4×C22⋊C4—24no—
183C2×#95—24no—
184C2×#95—44no—
185C2×#95C2312yes—
186C2×#95C2311yescharacteristic
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C25C2412yes—
233C25C2411yescharacteristic
234C22×Q8—22no—
235C22×Q8—24no—
236C22×Q8—42no—
237C22×Q8—41no—
238C22×Q8—41no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—41no—
247C22×D4—41no—
248C22×D4C2×D418yes—
249C22×D4C2×D414yes—
250C22×D4#4118yes—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—41no—
268C23×C4—41no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—41no—
280C23×C4—42no—
281C23×C4—41no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4C2×D414yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304#124—416no—
305C22⋊Q8—416no—
306#121—232no—
307C4×D4—416no—
308C4×D4—432no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4C2×D414yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4C2×D418yes—
389C2×C22⋊C4#4114yes—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—42no—
396C2×C42—42no—
397#95—24no—
398#95—24no—
399#95—22no—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—41no—
423#95—41no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24C22×D414yes—
465C24C22×D412yes—
466C24C2×#4114yes—
467C24C2×#4114yes—
468C24C2×#4112yes—
469C242−1+412yes—
470C24C2511yescharacteristic
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—84no—
475C2×Q8—84no—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—44no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4#123116yes—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—44no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—82no—
611C22×C4—84no—
612C22×C4—82no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4—84no—
623C22×C4C22×D414yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4H(5,𝔽2)14yes—
629C22×C4H(5,𝔽2)14yes—
630C22×C42−1+412yes—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—84no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4—84no—
640C4⋊C4—84no—
641C4⋊C4—84no—
642C22⋊C4—216no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C22⋊C4—44no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—44no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C22⋊C4—82no—
659C42—48no—
660C42—44no—
661C42—44no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23C2×#12318yes—
719C23#54714yes—
720C23C23×D411yescharacteristic
721C23C22×#4112yes—
722C23C22×#4111yescharacteristic
723C23C2×H(5,𝔽2)12yes—
724C23C2×H(5,𝔽2)12yes—
725C23C2×2−1+411yescharacteristic
726C23C2×2−1+411yescharacteristic
727C23#58511yescharacteristic
728C23#58511yescharacteristic
729C23#58511yescharacteristic
730C23#58512yes—
731Q8—88no—
732D4—416no—
733D4—432no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—88no—
841C2×C4—88no—
842C2×C4—816no—
843C2×C4—816no—
844C2×C4—816no—
845C2×C4—88no—
846C2×C4C2×#12314yes—
847C22—28no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—28no—
852C22—28no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—42no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—42no—
868C22—44no—
869C22—42no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22C22×#12311yescharacteristic
874C22#346111yescharacteristic
875C22C2×#54711yescharacteristic
876C22#348112yes—
877C22#348411yescharacteristic
878C22#348411yescharacteristic
879C22#348511yescharacteristic
880C22#348911yescharacteristic
881C22#349111yescharacteristic
882C22#350011yescharacteristic
883C22#350512yes—
884C22#350512yes—
885C22#351412yes—
886C22#351512yes—
887C22#352012yes—
888C22#352112yes—
889C22#353312yes—
890C22#353612yes—
891C22#354112yes—
892C22#354212yes—
893C22#354512yes—
894C22#356311yescharacteristic
895C22#356411yescharacteristic
896C4—24no—
897C4—42no—
898C4—44no—
899C4—44no—
900C4—42no—
901C4—44no—
902C4—44no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—81no—
907C4—82no—
908C4—82no—
909C4—81no—
910C4—82no—
911C4—82no—
912C4—81no—
913C2—48no—
914C2—44no—
915C2#3535111yescharacteristic
916C2#3606711yescharacteristic
917C2#3623711yescharacteristic
918C2#3776311yescharacteristic
919C2#4037612yes—
920C2#4382812yes—
921C2#4389211yescharacteristic
922C2#4681411yescharacteristic
923C2#4711912yes—
924C2#4914212yes—
925C2#4954611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #16429C2semidirect
4. #16365C2semidirect
5. #16066C2semidirect
6. #15954C2semidirect
7. #15541C2semidirect
8. #15454C2semidirect
9. #15383C2semidirect
10. #15339C2semidirect
11. #15063C2semidirect
12. #14934C2semidirect
13. #14860C2semidirect
14. #14767C2semidirect
15. #14473C2semidirect
17. #14040C2semidirect
18. #14016C2semidirect
19. #13975C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#24272
C2×#23252
#164292
#163652
#160662
#159542
#155412
#154542
#153832
#153392
#150632
#149342
#148602
#147672
#144732
#144172
#140402
#140162
#139752